tests

chore: add check for closed connector #5808

Job	Run time
unit tests (3.14)	1m 10s
unit tests (3.10)	1m 12s
integration tests (macos-latest, 3.14)	1m 55s
integration tests (windows-latest, 3.10)	1m 41s
integration tests (windows-latest, 3.14)	2m 22s
integration tests (ubuntu-latest, 3.10)	1m 26s
integration tests (ubuntu-latest, 3.14)	59s
integration tests (macos-latest, 3.10)	1m 41s
	12m 26s

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